As a catalyst system which can be used in the trimerization, oligomerization or polymerization reaction of an olefin, a catalyst system comprising a metal source pyrrole-containing compound and a metal alkyl is known (see Japanese Patent Kokai (Laid-Open) No. 6-239920).
Under these circumstances, an object to be accomplished by the present invention is to provide a novel catalyst system which can be preferably used in the trimerization, oligomerization or polymerization reaction of an olefin, and a method for the trimerization, oligomerization or polymerization reaction of an olefin, which comprises using the catalyst system.